Stent implantation alters coronary artery hemodynamics and wall shear stress during maximal vasodilation.

Coronary stents improve resting blood flow and flow reserve in the presence of stenoses, but the impact of these devices on fluid dynamics during profound vasodilation is largely unknown. We tested the hypothesis that stent implantation affects adenosine-induced alterations in coronary hemodynamics and wall shear stress in anesthetized dogs (n = 6) instrumented for measurement of left anterior descending coronary artery (LAD) blood flow, velocity, diameter, and radius of curvature. Indexes of fluid dynamics and shear stress were determined before and after placement of a slotted-tube stent in the absence and presence of an adenosine infusion (1.0 mg/min). Adenosine increased blood flow, Reynolds (Re) and Dean numbers (De), and regional and oscillatory shear stress concomitant with reductions in LAD vascular resistance and segmental compliance before stent implantation. Increases in LAD blood flow, Re, De, and indexes of shear stress were observed after stent deployment (P < 0.05). Stent implantation reduced LAD segmental compliance to zero and potentiated increases in segmental and coronary vascular resistance during adenosine. Adenosine-induced increases in coronary blood flow and reserve, Re, De, and regional and oscillatory shear stress were attenuated after the stent was implanted. The results indicate that stent implantation blunts alterations in fluid dynamics during coronary vasodilation in vivo.     

Modeling the bifurcating flow in a CT-scanned human lung airway

The inspiratory flow characteristics in a CT-scanned human lung model were numerically investigated using low Reynolds number (LRN) kappa-omega turbulent model. The five-generation airway is extracted from the trachea to segmental bronchi of a 60-year-old Chinese male patient. Computations were carried out in the Reynolds number range of 900-2100, corresponding to mouth-air breathing rates of 190-440ml/s. Flow patterns on the Re=2100 and flow rate distribution were presented. In this model, the flow pattern is very complex. To count the effect of laryngeal jet on trachea inlet, the trachea was extended and modified to simulate the larynx, consequently the inlet velocity profile is biased towards the rear wall. In the inferior lobar bronchi, there are two stems in which the axial velocity is stronger but secondary velocity is weaker. Secondary flow in the lateral bronchi is stronger than the medial ones. With increasing Re, the air flow increases in the middle, inferior lobes and left main bronchus, i.e., flow biases to left and downward.     

Computational analysis of confined jet flow and mass transport in a blind tube.

A computational analysis of confined nonimpinging jet flow in a blind tube is performed as an initial investigation of the underlying fluid and mass transport mechanics of tracheal gas insufflation. A two-dimensional axisymmetric model of a laminar steady jet flow into a concentric blind-end tube is put forth and the governing continuity, momentum, and convection-diffusion equations are solved with a finite element code. The effects of the jet diameter based Reynolds number (Re(j)), the ratio of the jet-to-outer tube diameters (epsilon), and the Schmidt number (Sc) are evaluated with the determined velocity and contaminant concentration fields. The normalized penetration depth of the jet is found to increase linearly with increasing Re(j) for epsilon = O(0.1). For a given epsilon, a ring vortex that develops is observed to be displaced downstream and radially outward from the jet tip for increasing Re(j). The axial shear stress profile along the inside wall of the outer tube possesses regions of fixed shear stress in addition to a local minimum and maximum in the vicinity of the jet tip. Corresponding regions of axial shear stress gradients exist between the fixed shear stress regions and the local extrema. Contaminant concentration gradients develop across the ring vortex indicating the inward diffusion of contaminant into the jet flow. For fixed epsilon and Sc and Re(j) approximately 900, normalized contaminant flow rate is observed to be approximately twice that of simple diffusion. This model predicts modest net axial contaminant transport enhancement due to convection-diffusion interaction in the region of the ring vortex.     

The influence of inlet velocity profile on predicted flow in type B aortic dissection

In order for computational fluid dynamics to provide quantitative parameters to aid in the clinical assessment of type B aortic dissection, the results must accurately mimic the hemodynamic environment within the aorta. The choice of inlet velocity profile (IVP) therefore is crucial; however, idealised profiles are often adopted, and the effect of IVP on hemodynamics in a dissected aorta is unclear. This study examined two scenarios with respect to the influence of IVP—using (a) patient-specific data in the form of a three-directional (3D), through-plane (TP) or flat IVP; and (b) non-patient-specific flow waveform. The results obtained from nine simulations using patient-specific data showed that all forms of IVP were able to reproduce global flow patterns as observed with 4D flow magnetic resonance imaging. Differences in maximum velocity and time-averaged wall shear stress near the primary entry tear were up to 3% and 6%, respectively, while pressure differences across the true and false lumen differed by up to 6%. More notable variations were found in regions of low wall shear stress when the primary entry tear was close to the left subclavian artery. The results obtained with non-patient-specific waveforms were markedly different. Throughout the aorta, a 25% reduction in stroke volume resulted in up to 28% and 35% reduction in velocity and wall shear stress, respectively, while the shape of flow waveform had a profound influence on the predicted pressure. The results of this study suggest that 3D, TP and flat IVPs all yield reasonably similar velocity and time-averaged wall shear stress results, but TP IVPs should be used where possible for better prediction of pressure. In the absence of patient-specific velocity data, effort should be made to acquire patient’s stroke volume and adjust the applied IVP accordingly.

     

Analysis of blood flow in an out-of-plane CABG model

Coronary artery bypass graft (CABG) is a routine surgical treatment for ischemic and infarcted myocardium. A large number of CABG fail postoperatively because of intimal hyperplasia within months or years. The cause of this failure is thought to be partly related to the flow patterns and shear stresses acting on the endothelial cells. An accurate representation of the flow field and associated wall shear stress (WSS) requires a detailed three-dimensional (3D) model of the CABG. The purpose of this study is to present a detailed analysis of blood flow in a 3D aorto/left CABG, bypassing the occluded left anterior descending coronary (LAD) artery. The analysis takes into account the influence of the out-of-plane geometry of the graft. The finite volume technique was employed to model the 3D blood flow pattern to determine the velocity and WSS distributions. This study presents the flow field distributions of the velocity and WSS at four instances of the cardiac cycle, two in systole and two in diastole. Our results reveal that the CABG geometry has a significant effect on the velocity distribution. The axial velocity profiles at different instances of the cardiac cycle exhibit strong skewing; significant secondary flow and vortex structures are seen in the in-plane velocity patterns. The maximum WSS on the bed of the occluded LAD artery opposite to the graft junction is 14 Pa in middiastole, whereas there is a significantly lower and more uniform distribution of WSS on the bed of the anastomosis. The present results indicate that nonplanarity of the blood vessel along with the inflow conditions has a substantial effect on the fluid mechanics of CABG that contribute to the patency of graft.     

The effect of blood viscoelasticity on pulsatile flow in stationary and axially moving tubes

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient ▿P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The ▿P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published ▿P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.     

Frequency dependence of dynamic curvature effects on flow through coronary arteries

The flow through a curved tube model of a coronary artery was investigated computationally to determine the importance of time-varying curvature on flow patterns that have been associated with the development of atherosclerosis. The entry to the tube was fixed while the radius of curvature varied sinusoidally in time at a frequency of 1 or 5 Hz. Angiographic data from other studies suggest that the radius of curvature waveform contains significant spectral content up to 6 Hz. The overall flow patterns were similar to those observed in stationary curved tubes; velocity profile skewed toward the outer wall, secondary flow patterns, etc. The effects of time-varying curvature on the changes in wall shear rate were expressed by normalizing the wall shear rate amplitude with the shear rate calculated at the static mean radius of curvature. It was found that the wall shear rate varied as much as 94 percent of the mean wall shear rate at the mid wall of curvature for a mean curvature ratio of 0.08 and a 50 percent change in radius of curvature. The effects of 5 Hz deformation were not well predicted by a quasi-static approach. The maximum values of the normalized inner wall shear rate amplitude were found to scale well with a dimensionless parameter equivalent to the product of the mean curvature ratio (delta), normalized change in radius of curvature (epsilon), and a Womersley parameter (alpha). This parameter was less successful at predicting the amplitudes elsewhere in the tube, thus additional studies are necessary. The mean wall shear rate was well predicted with a static geometry. These results indicate that dynamic curvature plays an important role in determining the inner wall shear rates in coronary arteries that are subjected to deformation levels of epsilon delta alpha > 0.05. The effects were not always predictable with a quasi-static approach. These results provide guidelines for constructing more realistic models of coronary artery flow for atherogenesis research.     

Velocity and wall shear stress patterns in the human right coronary artery.

Blood flow dynamics in the human right coronary artery have not been adequately quantified despite the clinical significance of coronary atherosclerosis. In this study, a technique was developed to construct a rigid flow model from a cast of a human right coronary artery. A laser photochromic method was used to characterize the velocity and wall shear stress patterns. The flow conditions include steady flow at Reynolds numbers of 500 and 1000 as well as unsteady flow with Womersley parameter and peak Reynolds number of 1.82 and 750, respectively. Characterization of the three-dimensional geometry of the artery revealed that the largest spatial variation in curvature occurred within the almost branch-free proximal region, with the greatest curvature existing along the acute margin of the heart. In the proximal segment, high shear stresses were observed on the outer wall and lower, but not negative, stresses along the inner wall. Low shear stress on the inner wall may be related to the preferential localization of atherosclerosis in the proximal segment of the right coronary artery. However, it is possible that the large difference between the outer and inner wall shear stresses may also be involved.     

Measurement and prediction of flow through a replica segment of a mildly atherosclerotic coronary artery of man

Pressure distributions were measured along a hollow vascular axisymmetric replica of a segment of the left circumflex coronary artery of man with mildly atherosclerotic diffuse disease. A large range of physiological Reynolds numbers from about 60 to 500, including hyperemic response, was spanned in the flow investigation using a fluid simulating blood kinematic viscosity. Predicted pressure distributions from the numerical solution of the Navier-Stokes equations were similar in trend and magnitude to the measurements. Large variations in the predicted velocity profiles occurred along the lumen. The influence of the smaller scale multiple flow obstacles along the wall (lesion variations) led to sharp spikes in the predicted wall shear stresses. Reynolds number similarity was discussed, and estimates of what time averaged in vivo pressure drop and shear stress might be were given for a vessel segment.     

Flow measurements in a human femoral artery model with reverse lumen curvature

Flow visualization and wall pressure measurements were made in a smooth reverse curvature model that conformed to the gentle "s" shape of a left femoral artery angiogram of a patient in a clinical trial. Observed lesion localization at the inner (lesser) curvatures appeared to be associated with secondary flows in the wall vicinity directed toward the inner curvatures that tended to reverse direction in the flow entering the reverse curvature region. Moderate flow resistance increases of about 20 percent above the Poiseuille flow relation were found at the higher physiological Reynolds numbers Re above about 600-700 and thus Dean numbers for steady flow. For pulsatile flow simulation, flow resistances did not increase up to the largest Re of 470 tested. Apparently, the large variations in velocity during the cardiac cycle disrupted the stronger secondary flow patterns observed at the higher Reynolds numbers for steady flow.     

Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses

Non-Newtonian fluid flow in a stenosed coronary bypass is investigated numerically using the Carreau-Yasuda model for the shear thinning behavior of the blood. End-to-side coronary bypass anastomosis is considered in a simplified model geometry where the host coronary artery has a 75% severity stenosis. Different locations of the bypass graft to the stenosis and different flow rates in the graft and in the host artery are studied. Particular attention is given to the non-Newtonian effect of the blood on the primary and secondary flow patterns in the host coronary artery and the wall shear stress (WSS) distribution there. Interaction between the jet flow from the stenosed artery and the flow from the graft is simulated by solving the three-dimensional Navier-Stokes equation coupled with the non-Newtonian constitutive model. Results for the non-Newtonian flow, the Newtonian flow and the rescaled Newtonian flow are presented. Significant differences in axial velocity profiles, secondary flow streamlines and WSS between the non-Newtonian and Newtonian fluid flows are revealed. However, reasonable agreement between the non-Newtonian and the rescaled Newtonian flows is found. Results from this study support the view that the residual flow in a partially occluded coronary artery interacts with flow in the bypass graft and may have significant hemodynamic effects in the host vessel downstream of the graft. Non-Newtonian property of the blood alters the flow pattern and WSS distribution and is an important factor to be considered in simulating hemodynamic effects of blood flow in arterial bypass grafts.     

Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery

The endothelial cells (ECs) lining a blood vessel wall are exposed to both the wall shear stress (WSS) of blood flow and the circumferential strain (CS) of pulsing artery wall motion. These two forces and their interaction are believed to play a role in determining remodeling of the vessel wall and development of arterial disease (atherosclerosis). This study focused on the WSS and CS dynamic behavior in a compliant model of a coronary artery taking into account the curvature of the bending artery and physiological radial wall motion. A three-dimensional finite element model with transient flow and moving boundaries was set up to simulate pulsatile flow with physiological pressure and flow wave forms characteristic of the coronary arteries. The characteristic coronary artery curvature and flow conditions applied to the simulation were: aspect ratio (lambda) = 10, diameter variation (DV) = 6 percent, mean Reynolds number (Re) = 150, and unsteadiness parameter (alpha) = 3. The results show that mean WSS is about 50 percent lower on the inside wall than the outside wall while WSS oscillation is stronger on the inside wall. The stress phase angle (SPA) between CS and WSS, which characterizes the dynamics of the mechanical force pattern applied to the endothelial cell layer, shows that CS and WSS are more out of phase in the coronaries than in any other region of the circulation (-220 deg on the outside wall, -250 deg on the inside wall). This suggests that in addition to WSS, SPA may play a role in localization of coronary atherosclerosis.     

Computation of hemodynamics in the left coronary artery with variable angulations

The purpose of this study was to investigate the hemodynamic effect of variations in the angulations of the left coronary artery, based on simulated and realistic coronary artery models. Twelve models consisting of four realistic and eight simulated coronary artery geometries were generated with the inclusion of left main stem, left anterior descending and left circumflex branches. The simulated models included various coronary artery angulations, namely, 15°, 30°, 45°, 60°, 75°, 90°, 105° and 120°. The realistic coronary angulations were based on selected patient's data with angles ranging from narrow angles of 58° and 73° to wide angles of 110° and 120°. Computational fluid dynamics analysis was performed to simulate realistic physiological conditions that reflect the in vivo cardiac hemodynamics. The wall shear stress, wall shear stress gradient, velocity flow patterns and wall pressure were measured in simulated and realistic models during the cardiac cycle. Our results showed that a disturbed flow pattern was observed in models with wider angulations, and wall pressure was found to reduce when the flow changed from the left main stem to the bifurcated regions, based on simulated and realistic models. A low wall shear stress gradient was demonstrated at left bifurcations with wide angles. There is a direct correlation between coronary angulations and subsequent hemodynamic changes, based on realistic and simulated models. Further studies based on patients with different severities of coronary artery disease are required to verify our results.     

Two-dimensional color-mapping of turbulent shear stress distribution downstream of two aortic bioprosthetic valves in vitro.

Since artificial heart valve related complications such as thrombus formation, hemolysis and calcification are considered related to flow disturbances caused by the inserted valve, a thorough hemodynamic characterization of heart valve prostheses is essential. In a pulsatile flow model, fluid velocities were measured one diameter downstream of a Hancock Porcine (HAPO) and a Ionescu-Shiley Pericardial Standard (ISPS) aortic valve. Hot-film anemometry (HFA) was used for velocity measurements at 41 points in the cross-sectional area of the ascending aorta. Three-dimensional visualization of the velocity profiles, at 100 different instants during one mean pump cycle, was performed. Turbulence analysis was performed as a function of time by calculating the axial turbulence energy within 50 ms overlapping time windows during the systole. The turbulent shear stresses were estimated by using the correlation equation between Reynolds normal stress and turbulent (Reynolds) shear stress. The turbulent shear stress distribution was visualized by two-dimensional color-mapping at different instants during one mean pump cycle. Based on the velocity profiles and the turbulent shear stress distribution, a relative blood damage index (RBDI) was calculated. It has the feature of combining the magnitude and exposure time of the estimated shear stresses in one index, covering the entire cross-sectional area. The HAPO valve showed a skewed jet-type velocity profile with the highest velocities towards the left posterior aortic wall. The ISPS valve revealed a more parabolic-shaped velocity profile during systole. The turbulent shear stresses were highest in areas of high or rapidly changing velocity gradients. For the HAPO valve the maximum estimated turbulent shear stress was 194 N m-2 and for the ISPS valve 154 Nm-2. The RBDI was the same for the two valves. The turbulent shear stresses had magnitudes and exposure times that might cause endothelial damage and sublethal or lethal damage to blood corpuscules. The RBDI makes comparison between different heart valves easier and may prove important when making correlation with clinical observations.     

An experimental analysis of the flow field in a three-dimensional model of the human carotid artery bifurcation

Steady flow measurements were carried out in a rigid three-dimensional model of the human carotid artery bifurcation at a Reynolds number of 640 and a flow division ratio of 50/50. Both axial and secondary velocities were measured with a laser-Doppler anemometer. In the bulb opposite to the flow divider a zone with negative axial velocities was found with a maximal diameter of about 60% of the local diameter of the branch and a cross-sectional extent of about 25% of the local cross-sectional area. In the bulb the maximum axial velocity shifted towards the divider wall and at the end of the bulb an axial velocity plateau arose near the non-divider wall. Halfway through the bulb, secondary flow showed a vortex through which fluid flowed towards the divider wall near the bifurcation plane and back towards the non-divider wall near the upper walls.     

Flow-pressure drop measurement and calculation in a tapered femoral artery of a dog

This study describes the in vivo measurement of pressure drop and flow during the cardiac cycle in the femoral artery of a dog, and the computer simulation of the experiment based on the use of the measured flow, vessel dimensions and blood viscosity. In view of the experimental uncertainty in obtaining the accurate velocity profile at the wall region, the velocity pulse at the center was measured and numerical calculations were performed for the center Une instantaneous velocity and within the two limits of spatial distribution of inlet flow conditions: uniform and parabolic. Temporal and spatial variations of flow parameters, i.e., velocity profile, shear rate, non-Newtonian viscosity, wall shear stress, and pressure drop were calculated. There existed both positive and negative shear rates during a pulse cycle, i.e., the arterial wall experiences zero shear three times during a cardiac cycle. For the parabolic inlet condition, the taper of the artery not only increased the magnitude of the positive and negative shear rates, but caused a steep gradient in shear rate, a phenomenon which in turn affects wall shear stress and pressure. In contrast, for the uniform inlet condition, the flow through the tapered artery was predominantly the developing type, which resulted in reduction in magnitude of wall shear rate along the axial direction.     

Developing pulsatile flow in a deployed coronary stent

A major consequence of stent implantation is restenosis that occurs due to neointimal formation. This patho-physiologic process of tissue growth may not be completely eliminated. Recent evidence suggests that there are several factors such as geometry and size of vessel, and stent design that alter hemodynamic parameters, including local wall shear stress distributions, all of which influence the restenosis process. The present three-dimensional analysis of developing pulsatile flow in a deployed coronary stent quantifies hemodynamic parameters and illustrates the changes in local wall shear stress distributions and their impact on restenosis. The present model evaluates the effect of entrance flow, where the stent is placed at the entrance region of a branched coronary artery. Stent geometry showed a complex three-dimensional variation of wall shear stress distributions within the stented region. Higher order of magnitude of wall shear stress of 530 dyn/cm2 is observed on the surface of cross-link intersections at the entrance of the stent. A low positive wall shear stress of 10 dyn/cm2 and a negative wall shear stress of -10 dyn/cm2 are seen at the immediate upstream and downstream regions of strut intersections, respectively. Modified oscillatory shear index is calculated which showed persistent recirculation at the downstream region of each strut intersection. The portions of the vessel where there is low and negative wall shear stress may represent locations of thrombus formation and platelet accumulation. The present results indicate that the immediate downstream regions of strut intersections are areas highly susceptible to restenosis, whereas a high shear stress at the strut intersection may cause platelet activation and free emboli formation.     

Wall shear stress and near-wall flows in the stenosed femoral artery

Stenotic artery hemodynamics are often characertised by metrics including oscillatory shear index (OSI) and residence time (RT). This analysis was conducted to clarify the link between the near-wall flow behaviour and these resultant flow metrics. A computational simulation was conducted of a stenosed femoral artery, with an idealised representative geometry and a physiologically realistic inlet profile. The overall flow behaviour was characterised through consideration of the axial flow, which was non-dimensionalised against mean flow velocity. The OSI and RT metrics, which are a useful indicator of likely atherosclerotic sites, were explained through a discussion of the WSS values at different time points, the velocity behaviour and velocity profiles, with a particular focus on the near-wall behaviour which influences wall shear stress and the transient evolution of the wall shear stress. While, the stenosis throat experiences high values of wall shear stress, the smooth flow through this contracted region results in low variation in wall shear stress vectors and limited opportunity for any particle stasis. However, regions were noted distal and proximal (though to a lesser extent), where the change in recirculation zones over the cycle created highly elevated regions of both OSI and RT.